Finite Group Databasebeta

← #11795963

Subgroups — #11795963

Order 1152.

713 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×C3⋊D3C211yesmaximal, characteristic
2C2×#63542C212yesmaximal, complemented
3C3×#4549C212yesmaximal, complemented
4#10589108C212yesmaximal, complemented
5D3×C22⋊C16—32nomaximal
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C32×C8C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C411yescharacteristic
9C2×C8×C3⋊D3—24no—
10C2×C8×C3⋊D3C411yescharacteristic
11C2×C8×C3⋊D3C411yescharacteristic
12C2×C8×C3⋊D3C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C3×C3⋊C16C2214yescomplemented
15#63542—24no—
16C22×D3×C8—32no—
17C22×D3×C8—61no—
18C2×D3×C16—34no—
19C3×C22⋊C16—32no—
20#4549D312yescomplemented
21(C2×D3)⋊C16—34no—
22C23×C3⋊D3C811yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C811yescharacteristic
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3C811yescharacteristic
28C2×C4×C3⋊D3C811yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C32×C8—22no—
32C2×C32×C8C2×C411yescharacteristic
33C2×C32×C8C2311yescharacteristic
34C2×C3⋊(C3⋊C8)—22no—
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3—22no—
38C8×C3⋊D3—22no—
39C8×C3⋊D3—22no—
40C8×C3⋊D3D414yes—
41C3×C3⋊C16—24no—
42C2×C22⋊C16—91noSylow
43C22×C4×D3—32no—
44C22×C4×D3—61no—
45C22×C3×C8—21no—
46C22×C3×C8C2×D312yes—
47C22×C3⋊C8—32no—
48C22×C3⋊C8—61no—
49C2×D3×C8—32no—
50C2×D3×C8—32no—
51C2×D3×C8—32no—
52C2×D3×C8—32no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55C2×D3×C8—61no—
56C2×D3×C8—61no—
57C2×D3×C8—68no—
58C2×D3×C8—68no—
59C2×C3×C16—34no—
60C2×C3⋊C16C2×D314yescomplemented
61D3×C16—68no—
62C23×C32C2×C811yescharacteristic
63C22×C3⋊D3—22no—
64C22×C3⋊D3—22no—
65C22×C3⋊D3C1614yescomplemented
66C22×C3⋊D3C2×C811yescharacteristic
67C22×C3⋊D3C2×C811yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4C2×C811yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3C2×C811yescharacteristic
74C2×C3⋊Dic3C2×C811yescharacteristic
75C4×C3⋊D3—22no—
76C4×C3⋊D3—21no—
77C4×C3⋊D3—21no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3C22⋊C412yes—
80C4×C3⋊D3M1612yes—
81C32×C8—21no—
82C32×C8C2×D412yes—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)C22⋊C412yes—
85C23×C8—91no—
86C22×C16—92no—
87C22⋊C16—32no—
88C22⋊C16—92no—
89C23×D3—32no—
90C23×D3—61no—
91C22×C3×C4—21no—
92C22×C3×C4C4×D312yes—
93C22×Dic3—32no—
94C22×Dic3—61no—
95C2×C4×D3—32no—
96C2×C4×D3—32no—
97C2×C4×D3—32no—
98C2×C4×D3—32no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C3×C8—24no—
108C2×C3×C8—24no—
109C2×C3×C8—21no—
110C2×C3×C8—21no—
111C2×C3×C8C4×D312yes—
112C2×C3×C8C22×D312yes—
113C2×C3⋊C8—32no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—64no—
118C2×C3⋊C8—64no—
119D3×C8—38no—
120D3×C8—64no—
121D3×C8—64no—
122D3×C8—64no—
123D3×C8—64no—
124D3×C8—64no—
125D3×C8—64no—
126D3×C8—64no—
127C3×C16—64no—
128C3⋊C16—24no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C1612yescomplemented
132C22×C32C22×C811yescharacteristic
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—28no—
136C2×C3⋊D3C22⋊C812yes—
137C2×C3⋊D3C2×C1612yes—
138C2×C3⋊D3C2×C1612yescomplemented
139C2×C3⋊D3M3212yes—
140C32×C4—21no—
141C32×C4C2×C22⋊C411yescharacteristic
142C32×C4C2×M1611yescharacteristic
143C3⋊Dic3—21no—
144C3⋊Dic3C22⋊C812yes—
145C23×C4—91no—
146C22×C8—91no—
147C22×C8—91no—
148C22×C8—91no—
149C22×C8—91no—
150C22×C8—91no—
151C22×C8—184no—
152C22×C8D3211yescharacteristic
153C2×C16—34no—
154C2×C16—184no—
155C23×C3—21no—
156C23×C3D3×C812yes—
157C22×D3—32no—
158C22×D3—38no—
159C22×D3—32no—
160C22×D3—64no—
161C22×D3—61no—
162C22×D3—61no—
163C22×D3—64no—
164C22×D3—64no—
165C22×D3—64no—
166C22×D3—64no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4D3×C812yes—
174C2×C3×C4C2×C4×D312yes—
175C2×Dic3—32no—
176C2×Dic3—32no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C4×D3—34no—
182C4×D3—34no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—62no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C3×C8—22no—
194C3×C8—22no—
195C3×C8—22no—
196C3×C8D3×D414yes—
197C3⋊C8—34no—
198C3⋊C8—62no—
199C3⋊C8—62no—
200C3⋊C8—62no—
201C2×C32—22no—
202C2×C32C2×C22⋊C811yescharacteristic
203C2×C32C22×C1611yescharacteristic
204C2×C32C2×M3211yescharacteristic
205C3⋊D3—22no—
206C3⋊D3C22⋊C1614yescomplemented
207C24—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—182no—
214C22×C4—182no—
215C22×C4#62411yescharacteristic
216C2×C8—22no—
217C2×C8—91no—
218C2×C8—94no—
219C2×C8—91no—
220C2×C8—182no—
221C2×C8—182no—
222C2×C8—182no—
223C2×C8—182no—
224C2×C8#62411yescharacteristic
225C2×C8C2×D3211yescharacteristic
226C16—64no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—21no—
233C22×C3D3×C1614yescomplemented
234C22×C3C2×D3×C812yes—
235C2×D3—34no—
236C2×D3—34no—
237C2×D3—34no—
238C2×D3—34no—
239C2×D3—62no—
240C2×D3—62no—
241C2×D3—62no—
242C2×D3—62no—
243C2×D3—616no—
244C2×D3—62no—
245C2×D3—616no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4D3×C22⋊C412yes—
254C3×C4D3×M1612yes—
255Dic3—34no—
256Dic3—62no—
257Dic3—62no—
258Dic3—62no—
259C32C2×C22⋊C1611yescharacteristic, complemented, Sylow
260C23—91no—
261C23—94no—
262C23—91no—
263C23—182no—
264C23—182no—
265C23#371011yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—91no—
269C2×C4—92no—
270C2×C4—92no—
271C2×C4—91no—
272C2×C4—182no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4#371011yescharacteristic
278C2×C4C2×#62411yescharacteristic
279C8—21no—
280C8—92no—
281C8—181no—
282C8#381112yes—
283C2×C3—24no—
284C2×C3—24no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3D3×C22⋊C812yes—
289C2×C3C2×D3×C1612yes—
290C2×C3D3×M3212yes—
291D3—38no—
292D3—64no—
293D3—64no—
294D3—64no—
295C22—21no—
296C22—21no—
297C22—92no—
298C22—92no—
299C22—92no—
300C22—92no—
301C22—188no—
302C22—181no—
303C22—181no—
304C22#6354212yescomplemented
305C22C2×#371011yescharacteristic
306C4—21no—
307C4—92no—
308C4—181no—
309C4#6381811yescharacteristic
310C4#6397411yescharacteristic
311C3—21no—
312C3D3×C22⋊C1612yescomplemented
313C2—22no—
314C2—94no—
315C2—182no—
316C2C2×#6354211yescharacteristic
317C2#1059062511yescharacteristic
318C2#1059115211yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutatorC2×C32C22×C16
FittingC22×C32×C8C22
socleC22×C32C22×C8
prime radicalC23×C3⋊D3C8
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32C2×C22⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#63542C2semidirect
3. C3×#4549C2semidirect
4. #10589108C2semidirect
14. C2×C3×C3⋊C16C22semidirect
20. #4549D3semidirect
60. C2×C3⋊C16C2×D3semidirect
65. C22×C3⋊D3C16semidirect
131. C22×C32C2×C16semidirect
138. C2×C3⋊D3C2×C16semidirect
206. C3⋊D3C22⋊C16semidirect
233. C22×C3D3×C16semidirect
259. C32C2×C22⋊C16semidirect
304. C22#63542semidirect
312. C3D3×C22⋊C16semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C8×C3⋊D32
C2×#635422
C3×#45492
#105891082
D3×C22⋊C163